Theory of Multi-Component Fluid Mixtures. I. Statistical Order-Disorder Analysis in Multi-Component Fluid Mixtures

Recent theories of solutions (Prigogine and co-workers; Scott) have been developed without specific reference to a molecular model by the use of a corresponding states procedure which relates the properties of the solution to the properties of one of the pure components. These considerations have been based exclusively upon intuitive postulates which have been formulated by analogy from previous ``cell'' theories of solutions. The basis for a corresponding states treatment is examined in a rigorous manner by the use of statistical mechanics. A general method is given for reducing the multi-component configurational partition function to a form peculiar to a system of one component. Two types of approximations to the rigorous theory that are amenable to numerical calculations are developed on a strictly mathematical basis, and are used to estimate the magnitudes of the correction terms to a corresponding states analysis.